Note that this worked even after completely re-installing Steam and Skyrim didn't. I suspect, but cannot be sure, this has something to do with Steam Cloud syncing because after attempting and failing to launch Skyrim I couldn't close Steam due to it.

After verification, there should be a patch that downloads. After the patch, it should work. So, before giving up after the verification completes, be sure to check your 'library' and make sure the patch has finished.
–
JClaspillNov 23 '11 at 15:57